In some formalism like DF, the sudden approximation is being used. The densities of the colliding nuclei are assumed to be unchanged at all distances during the overlapping process. The densities of two interacting nuclei overlap so that an increasing repulsive force would be expected due to this approximation and PEP. In some theoretical studies, this increase in energy of the dinuclear system is being simulated within a repulsive force in the NN interaction, and the nucleus-nucleus potential is being modified in consequence. Such modifications have been made mostly for fusion reactions, which led to the better reproduction of experimental data. For instance, it is shown that the incorporation of Pauli blocking properly with the DF model can achieve by taking into account the redefinition of the density matrices of the free isolated nuclei [1]}. Microscopically, from the standard M3Y potential developed with the density-dependent Pauli blocking potential of the density overlap of two colliding nuclei and consequent appearance some shallow pockets in \(\alpha \) -core potentials of \(\alpha \) +\(^{208}\) Pb, \(\alpha \) +\(^{197}\) Au, \(\alpha \) +\(^{209}\) Bi, and \(\alpha \) +\(^{238}\) U, their originated fusion cross-sections were consistent with the experimental data [2]}. Also, the simultaneous cross-section studies based on the experimental evidence for the reactions \(^{12}\) C + \(^{12}\) C, \(^{12}\) C + \(^{16}\) O, and \(^{16}\) O + \(^{16}\) O proposed a soft Gaussian repulsive core to the Woods-Saxon potential [3]}. Moreover, the unexpected steep falloff of fusion cross sections at energies far below the Coulomb barrier for the reactions \(^{64}\) Ni + \(^{64}\) Ni, \(^{58}\) Ni + \(^{58}\) Ni, and \(^{64}\) Ni + \(^{100}\) Mo were successfully explained by combination using the DF potential based on the M3Y interactions supplemented with a simulated repulsive core [4]}, [5]}.
